I am having a hard time with my strings; they keep breaking. I just put a new set on today, and before I could even get them tuned right, my G-3 and E-1 snapped. I'm smart enough to know not to crank them fast, I have been going slowly to let them stretch out. Also noticed at the end of the tuning peg, my D-4 looks as though its about to snap too.

|||||||||||-||||||||||||, basically how it looks wrapped around the peg.

If anyone can help me figure something out, that would be greatly appreciated.
Only two things I can think of are.... 1) are you tuning up too high (an octave up)..sorry if that's obvious. 2) if your diagram means you have ten turns above and ten turns below sandwiching the string going through the peg, try just two or three turns and see if that helps.
what kind of strings are you using?
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Tuning to the wrong octave is a common mistake; I've done it. (long ago...) Where are your strings breaking? Usually, string breakage is a mechanical problem. a sharp edge on the saddle, a burr or ding on the tuning machine post... Something like that.
First, follow the re-stringing guide at Frets.com.
When you take the strings off, check everything carefully...